"Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, thank to the pioneering works of Evans, Cohen, Morris and Searles on the violation of the second law, soon followed by the ground-breaking formulation of the Fluctuation Theorem by Gallavotti and Cohen for entropy fluctuation in the early nineties. Their work was by vast literature, both theoretical and experimental
The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an undergoing effort. Kurchan’s seminal work (2000) showed the measurement role has to be taken in account, leading to the introduction of the so called two-time measurement statistics (also known as full counting statistics). However in this context, the lack of a trajectory notion leads to both conceptual and technical problems, or phenomena with no classical counterpart, as underlined by some of our recent results.
In this talk I will review some of the key concept involved in the Fluctuation Theorem and its extensions to the quantum setting; I will present some recent results exploring the role played by ultraviolet regularity conditions (joint work with R.Raquépas and T.Benoist )."